Twinning (verbose reply)
Phil Jeffrey
phil at xtreme1.mskcc.org
Tue Feb 14 10:30:55 EST 1995
In article <3hnriq$qg3 at sun2.ruf.uni-freiburg.de> dikay at sun2.ruf.uni-freiburg.de (Kay Diederichs) writes:
>> : Hello,
>>
>> : I'd appreciate hearing from folks who have dealt with twinned crystals
>> : (not the obvious sort but the more subtle kind). In particular, how
>> : to tell if a particular crystal form is twinned, and any success in
>> : deconvoluting twinned data.
... (some stuff deleted) ...
>> 3) detwin the other data sets and proceed as usual, i.e. calculate
>> difference Pattersons to find heavy atom positions, and so on.
>> A small remaining twinning fraction, resulting from the fact that your
>> reference does not have alpha=0, does not hurt.
There are two problems working with de-twinned data that I wanted to bring up:
(1) as the twin fraction approaches 0.5, then the differences between
I(hkl) and I(h'k'l') get very small, approaching sigma for the reflections,
and detwinning becomes unreliable, since it's the I(hkl)-I(h'k'l') and the
estimate of the twin fraction that determine the detwinned intensities.
(2) the chances are that if your data is somewhat incomplete, then the
detwinning will make it even more incomplete since both I(hkl) and I(h'k'l')
must be observed to get either of the detwinned reflection intensities.
As for my experiences:
I worked on a problem in P2<1> with two Fab's in the asymmetric unit that
was twinned by hemimerohedry with twin fractions between 0.11 and 0.45. It
was a molecular replacement solution (by Axel Brunger, it's the example in
the X-PLOR manual) so I didn't have to work with heavy atom data. Because of
the data incompleteness issue, we ended up introducing the effects of twinning
into Fcalc during refinement (so we could use all the native data). Of course
one still needs to calculate the maps with de-twinned data. I'm not sure that
"twinning" Fcalc is all that stable a technique in refinement, and we only
did it in the later stages, after the model had converged against the twinned
or detwinned data. There is no truly satisfactory way to calculate derivatives
(dF/dX etc) with respect to twinned Fcalcs (at least I couldn't think of one).
We had an estimate of the initial twin fractions from the method of Britton
(plot the # of negative intensities in the de-twinned data vs twin fraction
used, and use the highest twin fraction that does not produce an unreasonable
number of negative intensities). Subsequently we estimated the twin fraction
in refinement by minimizing the residual between Fobs (twinned) and Fcalc
(twinning introduced) vs the twin fraction.
We were, however, assisted by the fact that the non-xtallographic symmetry
and the twinning operation were similar operators in reciprocal space (they
might act in different ways mathematically, but they both work to increase
the correlation between I(hkl) and I(h'k'l'), so I actually ignored the
twinning in the case where alpha=0.11 for most of the refinement). The
twinning-ignored maps were often better than the twin-corrected maps,
presumably because the data was more complete in the former case.
We were able to refine the antibody structures (26-10 and 26-10/R9) into the
17% range at 2.5A, so at least in this case the twinning did not prevent
structure determination/refinement. It was one of the earliest applications
of Axel's PC-refinement technique I believe.
Just my 2c
Good luck
Phil
--
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| Phil Jeffrey | |
| X-ray/Computer Manager, Crystallography Lab | If you lie to the compiler, |
| Memorial Sloan-Kettering Cancer Center, NYC | it will get its revenge |
| phil at xray2.mskcc.org, p-jeffrey at ski.mskcc.org | - Henry Spencer |
| Ph: (212) 639 2189 Fax: (212) 717 3066 | |
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